When I work on shutter priority to freeze some action, the aperture gets wide open. This is dof is very low - but I see some beautiful pictures which preserve dof and also capture motion well.
How is that done?

"any arbitrary" ... is what I doubt can be done. My RAW converter software can't do that, I can manipulate the data only to an extent and that's it then. Plus it will introduce noise, too, if you all underexpose and then pull it up in the RAW converter programme.

If flash doesn't reach (or is not liked overly much by the persons photographed, and I assume they do some kind of sport, considering what Gallery we're in here), and DOF is too shallow by what your camera decides on, you might need to up the ISO. I don't know what you work with, and from when high ISO will result in annoyingly much noise, but if frozen action is what you want to or need to achieve, then noise might be the lesser of your evils. If all else fails, you can put your photos through a noise reduction software. With a good focus (should be achieved as DOF will be deeper!) and a bit of USM later, you should be good. It's a lot of post work, though!

ETA: Oh, hang on, this isn't the Sports Gallery, after all, why did I think we were in the Sports Gallery... oh well. Is it NOT sports you want to photograph then?

but inorder for them to work you have to have the image data there to work with from the start - that means not over or underexposing areas of the shot. If a digital camera overexposes and area all it records is white with no details and the same for underexposed (save that all it records is black). Raw has a little more play at each end when compared to JPEGs but it still has limits.

Also as said if you want fast shutter speeds with a deeper depth of field you either have to boost local lighting or raise your ISO. If you see shots with a fast shutter speed and a high depth of field chances are they are either raising their ISO very high on a high grade camera body (where noise is less of a problem than on lower level camera bodies) or they are using a lighting setup whereby they can boost the local lighting on the subject enough to expose correctly without having to raise their ISO. Even just shooting in good lighting can help to achive this effect.

Also note that if you use a longer telephoto lens to shoot a shot from further away you can get more depth of field than if you shoot the shot closer to the subject.

I normally shoot in RAW
and this is another question, can you fix the exposure to any arbitrary value with RAW?

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Even a properly exposed RAW photograph you're very unlikely to get more than 2 stops (and most likely less than this) of play in either direction. Since it sounds like you want to underexpose (to increase shutter) then push the exposure in RAW you will probably get far less than that, depending on how far you underexpose. If you clip your shadows, or have any really deep shadows, when you push your exposure, you will see a bunch of noise, more noise than high ISO.

Like someone said, there is no free lunch, especially in photography. You want a small aperture and a fast shutter. There's nothing you can do except somehow increase the light wherever you're shooting (strobes, hot lights, etc) or increase your ISO. My rule of thumb is that I would rather have noise in the shot and get the effect that I want than to miss the shot because I'm afraid of a little noise. You can deal with noise in post. Other things are more difficult.

As I understand it, you will get an identical picture if you shoot a perfectly exposed scene at, lets say 3200 ISO, as you would if you shot it at 1600 ISO while deliberately underexposing by 1 stop and then upping the exposure by 1 stop from the RAW file in post. At least, I saw in a review for the canon 450d where the tested its "3200 ISO" noise capabilities by doing that, even though the camera only goes to 1600 ISO.

As I understand it, you will get an identical picture if you shoot a perfectly exposed scene at, lets say 3200 ISO, as you would if you shot it at 1600 ISO while deliberately underexposing by 1 stop and then upping the exposure by 1 stop from the RAW file in post. At least, I saw in a review for the canon 450d where the tested its "3200 ISO" noise capabilities by doing that, even though the camera only goes to 1600 ISO.

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I don't doubt that, but there's so many variables with that. Pushing the exposure in RAW on an underexposed shot will likely create far more noise in the shadows than if you'd just used a higher ISO. In addition, (from my own experiences, ymmv) a higher percentage of that noise is chroma noise which is extremely difficult (if not impossible, in certain circumstances) to remove. Bottom line is, no matter what you do, without more light in the scene, with what the OP wants to do, he's going to have to deal with some kind of noise.

As I understand it, you will get an identical picture if you shoot a perfectly exposed scene at, lets say 3200 ISO, as you would if you shot it at 1600 ISO while deliberately underexposing by 1 stop and then upping the exposure by 1 stop from the RAW file in post. At least, I saw in a review for the canon 450d where the tested its "3200 ISO" noise capabilities by doing that, even though the camera only goes to 1600 ISO.

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You sure that is right and that its not overexpose the shot by one stop? Only if ISO 3200 is the same as an underexposed 1600 bumped up in editing there would no no point of having ISO 3200 as you could just just expose ISO 1600 correctly and have a better result.

Of course overexposing is a problem with fast motion as often as not one is already trying to get as much shutter speed as possibly anyway - so overexposing is a tricky thing to achive in practice unless one is in very good lighting. Further whilst overexposing on the meter reading can give one more image data to work with it does put the highlights at even greater risk of blowing out which is of course not ideal .